Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2000-06-30
Choquet Theory in Metric SpacesT. Okon (1) Technische Universität Dresden, Germany
This paper deals with a generalization of the classical Choquet theorem. We consider metric spaces which are endowed with an abstract notion of convexity. Convex combinations are obtained by the solutions of variational inequalities. A generalized Krein-Milman theorem is derived from our Choquet theorem. We end with an example based on hyperbolic geometry.
Keywords: Abstract convexity in metric spaces, Choquet theorem, Krein-Milman theorem, hyperbolic geometry
Okon T.: Choquet Theory in Metric Spaces. Z. Anal. Anwend. 19 (2000), 303-314. doi: 10.4171/ZAA/952